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oai:mountainscholar.org:10217/2429102026-01-29T21:33:12Zcom_10217_100532com_10217_100000com_10217_100518com_10217_100303col_10217_100538col_10217_100519

Wang, Ying, author Davis, Richard A., advisor Boes, Duane C., committee member 2026-01-23T17:29:59Z 2002 ETDF_2002_Wang_3075392.pdf https://hdl.handle.net/10217/242910 https://doi.org/10.25675/3.025767 The focus of this thesis is on modeling time series of count data. We consider an extension of linear Gaussian state space models - parameter driven models in which th e mean function of a time series of observed counts {Yt} is specified bv a linear predictor modified by a 'latent process’. As in linear regression with correlated errors, there is a need for model diagnostic and identification techniques to decide if it is necessary to include a latent process in the specification of the mean of the Poisson counts and, if so, is there any evidence of autocorrelation in such a process. For a parameter driven model, the asymptotic distribution of standard generalized linear model estimators is derived for the case that an autocorrelated strong mixing latent process is present. Simple formulas for the effect of the autocovariance of the latent process on standard errors of the regression coefficients are also provided. A method of testing for the existence of a latent process is developed and compared to existing test statistics via simulation. Once the existence of a latent process has been detected, a simple and easily implementable method for estimating the autocovariance of the latent process is given. The standard errors of the estimates are also provided. Methods for adjusting for severe bias in previously proposed estimators of autocovariance are derived and their behavior investigated. A test statistic for testing serial dependence in the latent process is proposed based on the study of the distribution of autocorrelation estimates. The performance of different test statistics for testing serial dependence have been compared. Parameter estimation of a parameter driven model is complicated since the latent process is unobservable and the likelihood of the observed data y is an n-fold integral which does not have a simple closed form. Existing estimation methods involve intensive Monte Carlo simulation. A new estimation method that avoids Monte Carlo simulation is developed using an approximation to the likelihood of y. Applications of the methods to time series of monthly polio counts in the U.S . is used to illustrate the methods and results. A simulation study has been conducted to compare the performance of the various estimation methods. born digital doctoral dissertations English eng Colorado State University. Libraries 2000-2019 Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright. Per the terms of a contractual agreement, all use of this item is limited to the non-commercial use of Colorado State University and its authorized users. statistics Modeling time series of count data Text Doctor of Philosophy (Ph.D.) Doctoral Statistics Colorado State University This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). open.access